Introduction | Gallery of Just Intervals | Intervals larger than 2/1 | Links

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Introduction

In Just Intonation, a musical interval is specified as a ratio of two frequencies.. When two (or more) pitches are sounded that are in simple proportions to one another, there is a "fusing" quality to the sound which is often described as pleasing; hence the interest in tuning the pitches of musical systems according to such proportions. There is much debate as to what "consonance" means in a musical system, but in Just Intonation, it is generally assumed that lower numbers in frequency ratios lead to greater consonance. In the actual performance of a piece of music, the number of factors involved are enormous, and it is not often helpful to reduce a musical experience to a one-dimensional description of "consonance versus dissonance." Hence the need for this gallery, to give life to conversation about what an interval means beyond the numerical description: "5/3" or "21/16" or what have you.

What follows is a Gallery of Just Intervals in ascending order from 1/1 to 2/1 and beyond. No such list could possibly be complete (as there are infinite possible ratios), so please add intervals of interest as you see fit. Any rational interval is welcome, as long as the wiki author has some interest in it. Contributions to an interval's lore could include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, love letters, fan art, etc. If your contribution is unconventional, feel free to sign your name to it.

This page lists links to dedicated pages for each interval. Wiki page names are formatted "n_d" (where n is the numerator and d is the denominator of the interval) because both colons and slashes cannot be part of page names on wikispaces, but the links as they appear on the page are in the form n/d.

Explanation of the color names is here.

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Gallery of Just Intervals

See also List of Superparticular Intervals and List of intervals (Huygens-Fokker foundation)

frequency ratio	cents value (six decimal places)	color notation	some common names
1/1	0	w1 = white unison	unity, perfect prime, Tonic
32805/32768	1.953721	Ly-2 = yellow subcomma	schisma, |-15, 8, 1>
225/224	7.711523	ryy-2 = reddish-yellow subcomma	septimal subcomma, |-5, 2, 2, -1>
100/99	17.399484	ayy1 = amber deep yellow comma	Ptolemy's comma
99/98	17.576131	jrr-2 = jade deep red comma	Mothwellsma
2048/2025	19.552569	sgg2 = small deep green comma	|11, -4, -2>
81/80	21.506286	g1 = green comma	Syntonic comma, Didymus comma
531441/524288	23.460010	LLw-2 = white comma	Pythagorean comma, Ditonic comma, |-19, 12>
66/65	26.431568	ojg1 = oche-jadish comma	Winmeanma
65/64	26.841376	ey1 = emerald-yellow comma	Wilsorma, 13th-partial chroma
64/63	27.264092	r1 = red comma	Septimal comma, Archytas' comma
3125/3072	29.613568	Ly5-2 = quintuple yellow comma	Magic comma, small diesis, |-10, -1, 5>
50/49	34.975615	rryy-2 = deep reddish comma	septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis
49/48	35.696812	bb2 = deep blue comma	large septimal diesis, slendro diesis
45/44	38.905773	ay1 = amber-yellow comma	undecimal 1/5th tone
128/125	41.058858	g32 = triple green comma	Diesis, minor diesis, augmented comma, enharmonic comma, |7, 0, -3>
525/512	43.408335	Lyyb1 = large yellowish-yellow comma	Avicenna's enharmonic diesis, |-9, 1, 2, 1>
36/35	48.770381	gr1 = greenish comma	double comma, septimal quarter tone
250/243	49.166137	y31 = triple yellow comma	Porcupine comma, |1, -5, 3>
59049/57344	50.724102	Lr-2 = large red comma	Harrison's comma, |-13, 10, 0, -1>
100/97	52.732017	97qyy1 = 97esque deep yellow quarter-tone	shrutar quarter tone
33/32	53.272943	j1 = jade quarter-tone	undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
648/625	62.565148	g42 = quadruple green 2nd	diminished comma, major diesis, |8, 4, -4>
28/27	62.960904	b2 = blue 2nd	septimal chroma, small septimal chromatic semitone, septimal subminor second
25/24	70.672427	yy1 = deep yellow semitone	chroma, chromatic semitone, Zarlinian semitone
68/65	78.114034	17iog2 = 17ish ochre green 2nd	valentine semitone
22/21	80.537035	jr1 = jade-red semitone	undecimal minor semitone
64/61	83.115195	61q2 = 61esque 2nd	harry minor semitone
21/20	84.467193	bg2 = bluish 2nd	minor semitone, large septimal chromatic semitone
256/243	90.224996	sw2 = small white 2nd	Pythagorean limma, Pythagorean minor second, |8, -5>
135/128	92.178716	Ly1 = large yellow semitone	major limma, |-7, 3, 1>
18/17	98.954592	17q1 = 17esque semitone	small septendecimal semitone, Arabic lute index finger
17/16	104.955410	17i2 = 17ish 2nd	large septendecimal semitone, octave-reduced 17th harmonic
16/15	111.731285	g2 = green 2nd	diatonic semitone, classic minor second, octave-reduced 15th subharmonic
2187/2048	113.685006	Lw1 = large white semitone	apotome, |-11, 7>
77/72	116.233847	jb2 = jade-blue 2nd	undecimal secor
15/14	119.442808	ry1 = reddish semitone	septimal diatonic semitone
14/13	128.298245	ob2 = ochre-blue 2nd	2/3-tone, trienthird, tridecimal supraminor second
27/25	133.237575	gg2 = deep green 2nd	large limma
13/12	138.572661	e2 = emerald 2nd	tridecimal subtone, tridecimal 2/3-tone
243/224	140.949098	Lr1 = large red semitone	septimal subtone, |-5, 5, 0, -1>
88/81	143.497939	j2 = jade 2nd	undecimal subtone
49/45	147.428097	bbg3 = bluish-blue 3rd	swetismic neutral second
12/11	150.637059	a2 = amber 2nd	small undecimal neutral second, 3/4-tone
35/32	155.139620	yb2 = yellowish 2nd	septimal neutral second
78/71	162.786119	71qe2= 71esque emerald 2nd	porcupine neutral second
11/10	165.004228	jg2 = jadish 2nd	large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49	168.213190	rr1 = deep red augmented unison	Zalzal's mujannab
10/9	182.403712	y2 = yellow 2nd	minor whole tone
49/44	186.333871	abb3 = amber deep blue 3rd	werckismic minor second
19/17	192.557607	19i17q2 =19ish 17esque 2nd	quasi-meantone
28/25	196.198479	bgg3 = bluish-green 3rd	middle major second
55/49	199.979843	jrry1 = jade-red reddish unison	werckismic tone
9/8	203.910002	w2 = white 2nd	major whole tone, Pythagorean tone, octave-reduced 9th harmonic
17/15	216.686695	17ig3 = 17ish green 3rd	septendecimal whole tone, septendecimal eventone
8/7	231.174094	r2 = red 2nd	supermajor second, septimal whole tone, diminished third, octave-reduced 7th subharmonic
63/55	235.104252	abg3 = amber bluish 3rd	werckismic supermajor second
55/48	235.676655	jy2 = jade-yellow 2nd	keenanismic supermajor second
15/13	247.741053	oy2 = ochre-yellow 2nd	semifourth, tridecimal ultramajor second, tridecimal inframinor third
22/19	253.804926	19qj2 = 19esque jade 2nd	minimal minor third, godzilla third
64/55	262.368344	ag3 = amber-green 3rd	keenanismic subminor third, octave-reduced 55th subharmonic
7/6	266.870906	b3 = blue 3rd	subminor third, septimal minor third, augmented second
90/77	270.079867	ary2 = amber reddish 2nd	swetismic subminor third
62/53	271.531027	53q31i2 = 53esque 31ish 2nd	orwell subminor third
75/64	274.582429	yy2 = deep yellow 2nd	classic augmented second
20/17	281.358304	17qy2 = 17esque yellow 2nd	septendecimal augmented second, septendecimal minor third
13/11	289.209179	ea3 = emerald amber 3rd	tridecimal minor third
32/27	294.134997	w3 = white 3rd	Pythagorean minor third, octave-reduced 27th subharmonic
19/16	297.513016	19i3 = 19ish 3rd	otonal minor third, octave-reduced 19th harmonic
25/21	301.846520	ryy2 = reddish-yellow 2nd	quasi-tempered minor third
61/51	309.974395	61i17q2 = 61ish 17esque 2nd	myna third
6/5	315.641287	g3 = green 3rd	minor third, pental minor third
77/64	320.143849	jb3 = jade blue 3rd	keenanismic minor third, octave-reduced 77th harmonic
135/112	323.352810	ry2 = reddish aug 2nd	large septimal minor third, marvelous minor third, |-4, 3, 1, -1>
35/29	325.562426	29qyb3 = 29esque yellowish 3rd	doublewide minor third
17/14	336.129503	17ir3 = 17ish red 3rd	septendecimal supraminor third
73/60	339.520756	73ig3 = 73ish green 3rd	amity supraminor third
625/512	345.254855	Ly42 = large quadruple yellow 2nd	5-limit neutral third, |-9, 0, 4>
11/9	347.407941	j3 = jade 3rd	undecimal neutral third
60/49	350.616902	rry2 = reddish-red 2nd (aka p3 = purple 3rd)	smaller septimal neutral third
49/40	351.338099	bbg4 = bluish blue 4th (aka p3 = purple 3rd)	larger septimal neutral third
27/22	354.547060	a3 = amber 3rd	rastmic neutral third
16/13	359.472338	o3 = ochre 3rd	tridecimal neutral third
21/17	365.825498	17qb3 = 17esque blue 3rd	septendecimal submajor third
56/45	378.602191	bg4 = bluish 4th	narrow perde segah, marvelous major third
51/41	377.848005	41q17i4 = 41esque 17ish 4th	maja third
71/57	380.228526	71i19q3 = 71ish 19esque 3rd	witchcraft major third
76/61	380.628211	61q19i4 = 61esque 19ish 4th	magic major third
96/77	381.811152	ar3 = amber-red 3rd	undecimal perde segah, keenanismic major third
5/4	386.313714	y3 = yellow 3rd	major third, octave-reduced 5th harmonic, pental major third
81/64	407.820003	Lw3 = large white 3rd	Pythagorean major third, octave-reduced 81st harmonic
80/63	413.577806	ry3 = reddish 3rd	werckismic sharp major third
14/11	417.507964	ab4 = amber-blue 4th	undecimal major third, undecimal diminished fourth
32/25	427.372572	gg4 = deep green 4th	classic diminished fourth
77/60	431.875134	jbg4 = jade-bluish 4th	swetismic supermajor third
9/7	435.084095	r3 = red 3rd	supermajor third, septimal major third, septimal diminished fourth
31/24	443.080572	31i3 = 31ish 3rd	sensi supermajor third
22/17	446.362533	17qj3 = 17esque jade 3rd	septendecimal supermajor third
35/27	449.274618	yb4 = yellowish 4th	semi-diminished fourth
13/10	454.213948	eg4 = emerald-green 4th	Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third
64/49	462.348187	rr3 = deep red 3rd	septatonic major third
17/13	464.427748	17io4 = 17ish ochre 4th	septendecimal sub-fourth
21/16	470.780907	b4 = blue 4th	sub-fourth, narrow fourth, augmented third, 8ve-reduced 21st harmonic
33/25	480.645516	jgg4 = jadish green 4th	"5-EDO"-esque fourth
117/88	493.119721	ea4 = emerald amber 4th	tridecimal gentle fourth, |-3, 2, 0, 0, -1, 1>
4/3	498.044999	w4 = white 4th	just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
75/56	505.756522	ryy3 = reddish-yellow 3rd	marvelous fourth
27/20	519.551289	g4 = green 4th	acute fourth
19/14	528.687110	19ir4 = 19ish red 4th	19-limit wide fourth
49/36	533.741811	bb5 = deep blue 5th	Arabic lute acute fourth
15/11	536.950772	ay4 = amberish 4th	undecimal augmented fourth, subaugmented fourth
48/35	546.815381	gr4 = greenish 4th	septimal super-fourth
11/8	551.317942	j4 = jade 4th	super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
18/13	563.382340	o4 = ochre 4th	tridecimal augmented fourth
25/18	568.717426	yy4 = deep yellow 4th	classic augmented fourth, pental augmented fourth
88/63	578.582034	jr4 = jade-red 4th	werckismic augmented fourth
7/5	582.512193	bg5 = bluish 5th	augmented fourth, septimal tritone, Huygen's tritone
45/32	590.223716	y4 = yellow 4th
108/77	585.721154	ar4 = amber-red 4th	swetismic augmented fourth, |2, 3, 0, -1, -1>
24/17	596.999591	17q4 = 17esque 4th	smaller septendecimal tritone
17/12	603.000409	17i5 = 17ish 5th	larger septendecimal tritone
64/45	609.776284	g5 = green 5th
10/7	617.487807	ry4 = reddish 4th	diminished fifth, Euler's tritone, superaugmented fourth
23/16	628.274347	23i5 = 23ish 5th	23-limit superaugmented fourth, octave-reduced 23rd harmonic
36/25	631.282574	gg5 = deep green 5th	pental diminished fifth, classic diminshed fifth
13/9	636.617660	e5 = emerald 5th	tridecimal diminished fifth
16/11	648.682058	a5 = amber 5th	sub-fifth, octave-reduced 11th subharmonic
35/24	653.184619	yb5 = yellowish 5th	septimal sub-fifth
22/15	663.049228	jg5 = jadish 5th	undecimal diminished fifth, semidiminished fifth
72/49	666.258889	rr4 = deep red 4th	septimal catafifth
81/55	670.188347	ag5 = amber green 5th	undecimal catafifth
28/19	671.312890	19qb5 = 19esque blue 5th	19-limit narrow fifth
40/27	680.448711	y5 = yellow 5th	grave fifth
112/75	694.243478	bgg6 = bluish-green 6th	marvelous fifth
3/2	701.955001	w5 = white 5th	just perfect fifth, octave-reduced 3rd harmonic, diapente
182/121	706.717684	eaab6 = emerald blue deep amber 6th	tridecimal gentle fifth, |1, 0, 0, 1, -2, 1 >
176/117	706.880279	oj5 = ochre-jade 5th	tridecimal gentle fifth, |4, -2, 0, 0, 1, -1>
50/33	719.354484	ayy5 = amber deep yellow 5th	"5-EDO"-esque fifth
32/21	729.219093	r5 = red 5th	super-fifth, wide fifth, diminished sixth, octave-reduced 21st subharmonic
26/17	735.572252	17qe5 = 17esque emerald 5th	septendecimal super-fifth
49/32	737.651813	bb6 = deep blue 6th	superduper fifth, octave-reduced 49th harmonic
20/13	745.786052	oy5 = ochreish 5th	Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth
17/11	753.637467	17ia6 = 17ish amber 6th	septendecimal subminor sixth
14/9	764.915905	b6 = blue 6th	subminor sixth, septimal minor sixth, augmented fifth
25/16	772.627428	yy5 = deep yellow 5th	pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
11/7	782.492036	jr5 = jade-red 5th	undecimal subminor sixth, undecimal augmented fifth
63/40	786.422194	bg6 = bluish 6th
128/81	792.179997	sw6 = small white 6th
8/5	813.686286	g6 = green 6th	minor sixth, octave-reduced 5th subharmonic
413/256	827.997565	59ib6 = 59ish blue 6th	octave-reduced 413th harmonic, homestuck sixth (2-8 * 7 * 59)
13/8	840.527662	e6 = emerald 6th	tridecimal neutral sixth, octave-reduced 13th harmonic
80/49	848.661901	rryA5 = reddish-red 5th (aka p6 = purple 6th)
49/30	849.383198	bbg7 = bluish-blue 7th (aka p6 = purple 6th)
18/11	852.592059	a6 = amber 6th	undecimal neutral sixth
28/17	863.870497	17qb6 = 17esque blue 6th	septendecimal submajor sixth
5/3	884.358713	y6 = yellow 6th	major sixth
42/25	898.153480	bgg7 = bluish-green 7th
27/16	905.865003	w6 = white 6th	Pythagorean major sixth, octave-reduced 27th harmonic
22/13	910.790821	oj6 = ochre-jade 6th	tridecimal major sixth
17/10	918.641696	17ig7 = 17ish green 7th	septendecimal diminished seventh, septendecimal major sixth
12/7	933.129094	r6 = red 6th	supermajor sixth, septimal major sixth, diminished seventh
26/15	952.258947	eg7 = emeraldish 7th	semitwelfth, tridecimal inframinor seventh, tridecimal ultramajor sixth
7/4	968.825906	b7 = blue 7th	subminor seventh, harmonic seventh, augmented sixth, octave-reduced 7th harmonic
225/128	976.537429	Lyy6 = large deep yellow 6th	marvel five-limit harmonic seventh, octave-reduced 225th harmonic, |-7, 2, 2>
30/17	983.313305	17iy6 = 17ish yellow 6th	septendecimal minor seventh
16/9	996.089998	w7 = white 7th	Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
25/14	1003.801521	ryy6 = reddish-yellow 6th	Middle minor seventh
34/19	1007.442393	19q17i7 = 19esque 17ish 7th	Quasi-meantone minor seventh
9/5	1017.596288	g5 = green 7th	minor seventh, large minor seventh
29/16	1029.577194	29i7 = 29ish 7th	29-limit large minor seventh, octave-reduced 29th harmonic
20/11	1034.995772	ay7 = amberish 7th	undecimal minor seventh, small undecimal neutral seventh
64/35	1044.860380	gr7 = greenish 7th
11/6	1049.362941	j7 = jade 7th	undecimal neutral seventh, 21/4-tone
24/13	1061.427339	o7 = ochre 7th	tridecimal neutral seventh
13/7	1071.701755	er7 = emerald-red 7th	16/3-tone, tridecimal submajor seventh
28/15	1080.557192	bg8 = bluish octave	grave major seventh, octave minus a reddish aug unison
15/8	1088.268715	y7 = yellow 7th	major seventh, just major seventh, octave-reduced 15th harmonic
32/17	1095.044590	17q7 = 17esque 7th	small septendecimal major seventh, 8ve-reduced 17th subharmonic
17/9	1101.045408	17i8 = 17ish octave	large septendecimal major seventh
243/128	1109.775004	Lw7 = large white 7th	Pythagorean major seventh, octave-reduced 243rd harmonic
40/21	1115.532907	ry7 = reddish 7th	acute major seventh
61/32	1116.884905	61i7 = 61ish 7th	octave-reduced 61st harmonic
48/25	1129.327573	gg8 = deep green octave	octave minus a deep yellow augmented unison
27/14	1137.039096	r7 = red 7th
31/16	1145.035572	31i7 = 31ish 7th	31-limit ultramajor seventh, octave-reduced 31st harmonic
64/33	1146.727057	a8 = amber octave	octave-reduced 33rd subharmonic
35/18	1151.239619	yb8 = yellowish octave	octave minus a greenish comma
96/49	1164.303188	rr7 = deep red 7th
49/25	1165.024385	bbgg9 = deep bluish 9th
160/81	1178.493814	y8 = yellow octave	octave minus syntonic comma
2/1	1200	w8 = white octave	octave, diapason

Intervals larger than 2/1

frequency ratio	cents value (three decimal places)
13/6	1338.573
11/5	1365.004
16/7	1431.174
5/2	1586.314
8/3	1698.045
11/4	1751.318
16/5	2013.686
13/4	2040.528
10/3	2084.359
7/2	2168.826
11/3	2249.363
15/4	2288.269
4/1	2400.000
13/3	2538.573
9/2	2603.910
14/3	2666.871
5/1	2786.314
16/3	2898.045
11/2	2951.318
6/1	3101.955
13/2	3240.528
7/1	3368.826
15/2	3488.269
8/1	3600.000
9/1	3803.910
10/1	3986.314
11/1	4151.318
12/1	4301.955
13/1	4440.528
14/1	4568.826
15/1	4688.269
16/1	4800.000

Links

• Regions of the Interval Spectrum by Margo Schulter Permalink
• Manuel Op de Coul interval list*
• Anantomy of an Octave by Kyle Gann
• Alternative Tunings: Theory, Notation and Practice by Kite Giedraitis
• Stichting Huygens-Fokker: List of intervals